The Miami Heat, which won a second championship this year but has yet to pay Miami-Dade a dime in profits after 12 years at its bayfront arena, wants to extend its 30-year agreement with the county for another decade.

The existing agreement doesn’t expire until 18 years from now, in 2030. But, as permitted in the contract, Eric Woolworth, the team’s president of business operations, sent Mayor Carlos Gimenez a letter last week asking the county to begin negotiations on two five-year extensions.

The team wants to plan for its future at the county-owned AmericanAirlines Arena in downtown Miami, said Sammy Schulman, chief financial officer for the Heat Group, the team’s parent company.

The Heat’s request comes on the heels of a title-winning season that generated about $62 million in revenue — bringing it closer than ever to the threshold that would require the team’s arena-operating arm to fork over some of the money to the county. A separate entity handles Heat-related finances such as player salaries.

As part the county’s 1997 accord with the Heat, the team owned by Micky Arison financed construction on county land of the $213 million arena, which the team says ended up costing $239 million, after it bonded out a state sales-tax rebate. Miami-Dade agreed to let the arena keep profits up to $14 million a year, with the county set to receive 40 percent of any additional profits. The team has yet to reach that number since it debuted at the arena 12 years ago, essentially remaining at the facility rent-free.

Most of the Heat’s revenues have gone toward reimbursing the team for the money it borrowed to build the arena and to pay off past operating losses, with interest, as stipulated in the contract with the county. The arena ran a deficit through 2010; its finances improved with the arrival of LeBron James, the reigning league most valuable player.

Despite the team’s championship run last season, ticket and concession revenues at the arena dropped thanks to an NBA lockout that did away with about two months of basketball. Still, the team reported making $12.5 million in profit in the fiscal year that ended June 30.

The county also provides the arena with a $6.4 million annual subsidy, funded by taxes charged to hotel guests. The total paid out by the county so far: about $70 million. The building also receives a $2 million annual sales-tax rebate from the state.

All of the county terms could be tweaked as part of the negotiations, though the county says it’s too early to say which provisions it will focus on.

“There’s no real time crunch for this, at least contractually,” Deputy Mayor Ed Marquez said. “We’re amenable to discussing anything with our partners. I don’t know what they have in mind.”

Schulman, the team’s CFO, wouldn’t delve into specifics. The Heat’s lobbyist, lawyer Jorge Luis Lopez, who is close to Mayor Gimenez, called the profit-sharing provision “the elephant in the room.”

“All terms of the extension are on the table,” he said.

He added that the county may not be in a position to continue providing an annual subsidy to the arena, which would put a greater burden on the team to maintain the facility. That suggests that more revenues could go toward capital improvements and less toward potential profits to split with the county.

Though Schulman did not outline any particular future renovations, he made a point of noting that the arena has paid for about $40 million in upgrades over the years.

“The building’s almost 15 years old — we’re about halfway through the life of the building,” he said. “We plan to continue to keep it as a first-class facility, whatever that means, and keep investing in it.”

In a searing audit earlier this year, the county’s inspector general questioned $3.3 million the arena spent on capital improvements, saying the money should have gone toward negating team losses instead. Inspector General Christopher Mazzella also criticized various arena expenditures, including $12,300 in political contributions and $614,000 on lobbyists such as Lopez.

In its final response to the audit filed late last month, the county’s internal services department disagreed with Mazzella and said it would not seek to recoup any of that money, calling the capital improvements and the expenditures “customary” and “legitimate” business expenses.

The county administration and Basketball Properties Ltd., the Heat’s arena-operating arm, did agree to address 21 other inspector general recommendations aimed at bolstering Miami-Dade’s oversight of the arena management agreement.

The audit did not examine other aspects of the county’s deal with the team, including a 4.5-acre waterfront property behind the arena that the Heat had pledged to turn into a soccer park and baywalk. The promise came in the lead-up to a failed 1996 countywide referendum that gave voters a chance to deny construction of the arena.

The county, however, never required the team to commit to the park proposal. The Heat, which had gained control of the land as part of the arena deal, lost its rights to the property in 2004, after several development schemes failed to materialize.

But that doesn’t mean the Heat broke their promise to voters, the team’s Schulman said.

“We have more than delivered our end of the bargain here,” he said.

Schulman also said he’s not worried that his team will be tainted by public backlash against the Miami Marlins, which sold a slew of major players this month — a mere seven months after opening a new Little Havana ballpark funded mostly with public dollars. The Miami Dolphins have also expressed interest in public funding for a partial roof at the Sun Life football stadium in Miami Gardens.

In what could be a promising sign for the Heat, voters approved a referendum earlier this month allowing Sony Open tennis tournament organizers to begin talks with the county to extend the tournament’s lease and privately fund major upgrades to the Crandon Park tennis center in Key Biscayne.

To the Heat, the bigger picture is not what the arena pays Miami-Dade but the team’s broader contribution to the local economy. An economic-impact study commissioned by the team says the Heat and arena bring more than $1.4 billion and more than 21,000 jobs to the economy each year.

The study, by the Coral Gables-based Washington Economics Group, took into account not only $439 million in direct benefits, such as the team’s operating expenses and spending by out-of-town teams and visitors, but also “externalities” — intangible benefits “attributable to the presence of a successful sports franchise.” Those spillover effects included promoting Miami internationally, the team’s charitable contributions and building “civic pride.”